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Background: It is well known that effective nuclear interactions are in general nonlocal. Thus if nuclear densities obtained from ab initio no-core-shell-model (NCSM) calculations are to be used in reaction calculations, translationally invariant nonlocal densities must be available.Purpose: Though it is standard to extract translationally invariant one-body local densities from NCSM calculations to calculate local nuclear observables like radii and transition amplitudes, the corresponding nonlocal one-body densities have not been considered so far. A major reason for this is that the procedure for removing the center-of-mass component from NCSM wavefunctions up to now has only been developed for local densities.Results: A formulation for removing center-of-mass contributions from nonlocal one-body densities obtained from NCSM and symmetry-adapted NCSM (SA-NCSM) calculations is derived, and applied to the ground state densities of 4 He, 6 Li, 12 C, and 16 O. The nonlocality is studied as a function of angular momentum components in momentum as well as coordinate space. Conclusions:We find that the nonlocality for the ground state densities of the nuclei under consideration increases as a function of the angular momentum. The relative magnitude of those contributions decreases with increasing angular momentum. In general, the nonlocal structure of the one-body density matrices we studied is given by the shell structure of the nucleus, and can not be described with simple functional forms. PACS numbers: 21.60De,27.20.+n arXiv:1711.07080v1 [nucl-th] 19 Nov 2017where R nl (r) is the radial component of the single-particle harmonic oscillator wave function (defined in Appendix A). Using Eq. (7), the matrix elements of ρ sf ( r, r ) can be expressed as a sum over all tensors ρ ll K (r, r ), ρ sf ( r, r ) = Kll (−1) J −M J K J −M 0 M Y * l l K0 (r,r )ρ ll K (r, r ),separating out the radial and angular components of the nonlocal density.

Background: Calculating microscopic optical potentials for elastic nucleon-nucleus scattering has already led to large body of work in the past. For folding first-order calculations the nucleon-nucleon (NN) interaction and the one-body density of the nucleus were taken as input to rigorous calculations in a spectator expansion of the multiple scattering series.Purpose: Based on the Watson expansion of the multiple scattering series we employ a nonlocal translationally invariant nuclear density derived from a chiral next-to-next-to-leading order (NNLO) and the very same interaction for consistent full-folding calculation of the effective (optical) potential for nucleon-nucleus scattering for light nuclei.Methods: The first order effective (optical) folding potential is computed by integrating over the nonlocal, translationally invariant NCSM one-body density and the off-shell Wolfenstein amplitudes A and C. The resulting nonlocal potential serves as input for a momentum-space Lippmann-Schwinger equation, whose solutions are summed to obtain the nucleon-nucleus scattering observables. Results:We calculate scattering observables, such as total, reaction, and differential cross sections as well as the analyzing power and the spin-rotation parameter, for elastic scattering of protons and neutrons from 4 He, 6 He, 12 C, and 16 O, in the energy regime between 100 and 200 MeV projectile kinetic energy, and compare to available data.Conclusions: Our calculations show that the effective nucleon-nucleus potential obtained from the first-order term in the spectator expansion of the multiple scattering expansion describes experiments very well to about 60 degrees in the center-of-mass frame, which coincides roughly with the validity of the NNLO chiral interaction used to calculate both the NN amplitudes and the one-body nuclear density.

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